Table 4. Phenotypic vs. animal microbial correlations. Phenotypic correlations ($r_{pearson}$) and results from the bivariate microbial linear mixed model (bivariate extensions of model 1), with microbial covariance (${\sigma }_{m1,m2}$), and microbial correlation ($r_{m1,m2}$) with p values (standard errors are in in parenthesis).

Traitsa	Phenotypic correlation		Animal microbial correlation
	$r_{pearson}$	p value	${\sigma }_{m1,m2}$ (SE)	$r_{m1,m2}$ (SE)	p value
PU – FI	0.561	<0.001	5.695 (2.085)	0.905 (0.102)	<0.001
PU – BWG	0.581	<0.001	4.671 (1.637)	0.791 (0.116)	<0.001
PU – F:G	−0.387	<0.001	−0.310 (0.097)	−0.738 (0.134)	<0.001
FI – BWG	0.849	<0.001	3.743 (1.346)	0.902 (0.059)	<0.001
FI – F:G	−0.213	<0.001	−0.282 (0.076)	−0.876 (0.117)	<0.001
BWG – F:G	−0.645	<0.001	−0.302 (0.072)	−0.982 (0.028)	<0.001

^aFor trait abbreviations see Table 1.